Hepatocellular carcinoma (HCC) is graded mainly based on the characteristics of liver cell nuclei. This paper proposes a textural feature descriptor and a novel computational method for classifying liver cell nuclei and grading the HCC histological images. The proposed textural feature descriptor observes local and spatial characteristics of the texture patterns by using multifractal computation. The textural features are utilized for nuclear segmentation, fiber region detection, and liver cell nuclei classification. Four categories of nuclear features are computed such as texture, geometry, spatial distribution, and surrounding texture, for HCC classification. Significance of liver cell nuclei classification method is evaluated by classifying non-neoplastic and tumor tissues. Furthermore, characteristics of the liver cell nuclei were utilized for grading a set of HCC images into four classes and obtained 97.77% classification accuracy.